Problem: Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-x-2y &= -9 \\ 2x+2y &= 9\end{align*}$
Explanation: Begin by moving the $y$ -term in the second equation to the right side of the equation. $2x = -2y+9$ Divide both sides by $2$ to isolate $x$ $x = {-y + \dfrac{9}{2}}$ Substitute this expression for $x$ in the first equation. $-({-y + \dfrac{9}{2}}) - 2y = -9$ $y - \dfrac{9}{2} - 2y = -9$ Simplify by combining terms, then solve for $y$ $-1y - \dfrac{9}{2} = -9$ $-1y = -\dfrac{9}{2}$ $y = \dfrac{9}{2}$ Substitute $\dfrac{9}{2}$ for $y$ in the top equation. $-x-2( \dfrac{9}{2}) = -9$ $-x-9 = -9$ $-x = 0$ $x = 0$ The solution is $\enspace x = 0, \enspace y = \dfrac{9}{2}$.